Polynomial and kinetic differential equations

The right-hand side of the induced kinetic differential equation of reaction 

The proof of this theorem uses the form of the kinetic differential equation 

The consequence of the theorem as applied to the Lorenz equation is that no reaction can induce the Lorenz equation, and so this equation cannot be considered as the kinetic difiFerential equation of a complex chemical reaction. 

It is an astonishing fact that the converse of the theorem holds as well. If the right-hand side of a differential equation is an (M, M)-polynomial without negative cross-effects then it may be considered as the induced kinetic differential equation of a reaction, or, in other words, if there is no negative cross-effect in the right-hand side then there exists a reaction with the given equation as its deterministic model. 

A constructive proof of this theorem is stated as a problem one of the inducing reactions can easily be constructed. 

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